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Zhu Wang

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Published work

27 published item(s)

preprint2026arXiv

Balanced Edge Pruning for Graph Anomaly Detection with Noisy Labels

Graph anomaly detection (GAD) is widely applied in many areas, such as financial fraud detection and social spammer detection. Anomalous nodes in the graph not only impact their own communities but also create a ripple effect on neighbors throughout the graph structure. Detecting anomalous nodes in complex graphs has been a challenging task. While existing GAD methods assume all labels are correct, real-world scenarios often involve inaccurate annotations. These noisy labels can severely degrade GAD performance because, with anomalies representing a minority class, even a small number of mislabeled instances can disproportionately interfere with detection models. Cutting edges to mitigate the negative effects of noisy labels is a good option; however, it has both positive and negative influences and also presents an issue of weak supervision. To perform effective GAD with noisy labels, we propose REinforced Graph Anomaly Detector (REGAD) by pruning the edges of candidate nodes potentially with mistaken labels. Moreover, we design the performance feedback based on strategically crafted confident labels to guide the cutting process, ensuring optimal results. Specifically, REGAD contains two novel components. (i) A tailored policy network, which involves two-step actions to remove negative effect propagation step by step. (ii) A policy-in-the-loop mechanism to identify suitable edge removal strategies that control the propagation of noise on the graph and estimate the updated structure to obtain reliable pseudo labels iteratively. Experiments on three real-world datasets demonstrate that REGAD outperforms all baselines under different noisy ratios.

preprint2026arXiv

Learning Subspace-Preserving Sparse Attention Graphs from Heterogeneous Multiview Data

The high-dimensional features extracted from large-scale unlabeled data via various pretrained models with diverse architectures are referred to as heterogeneous multiview data. Most existing unsupervised transfer learning methods fail to faithfully recover intrinsic subspace structures when exploiting complementary information across multiple views. Therefore, a fundamental challenge involves constructing sparse similarity graphs that preserve these underlying subspace structures for achieving semantic alignment across heterogeneous views. In this paper, we propose a sparse attention graph learning (SAGL) method that learns subspace-preserving sparse attention graphs from heterogeneous multiview data. Specifically, we introduce a bilinear attention factorization scheme to capture asymmetric similarities among the high-dimensional features, which breaks the symmetry bottleneck that is inherent in the traditional representation learning techniques. A dynamic sparsity gating mechanism then predicts a feature-specific compression factor for adaptively controlling the topological contributions of neighbors. Furthermore, we employ a structured sparse projection via $α$-entmax to generate subspace-preserving sparse attention graphs for individual views. SAGL leverages these view-specific graphs to conduct sparse information aggregation, yielding discriminative representations for multiview learning tasks. In addition, we provide a rigorous theoretical analysis that bridges differentiable sparse attention and probability simplex constraints. Extensive experiments conducted on multiple benchmark datasets demonstrate that SAGL consistently outperforms the state-of-the-art unsupervised transfer learning approaches.

preprint2022arXiv

A Comparison of Neural Network Architectures for Data-Driven Reduced-Order Modeling

The popularity of deep convolutional autoencoders (CAEs) has engendered new and effective reduced-order models (ROMs) for the simulation of large-scale dynamical systems. Despite this, it is still unknown whether deep CAEs provide superior performance over established linear techniques or other network-based methods in all modeling scenarios. To elucidate this, the effect of autoencoder architecture on its associated ROM is studied through the comparison of deep CAEs against two alternatives: a simple fully connected autoencoder, and a novel graph convolutional autoencoder. Through benchmark experiments, it is shown that the superior autoencoder architecture for a given ROM application is highly dependent on the size of the latent space and the structure of the snapshot data, with the proposed architecture demonstrating benefits on data with irregular connectivity when the latent space is sufficiently large.

preprint2022arXiv

Estimating Atmospheric Parameters from LAMOST Low-Resolution Spectra with Low SNR

Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) acquired tens of millions of low-resolution stellar spectra. The large amount of the spectra result in the urgency to explore automatic atmospheric parameter estimation methods. There are lots of LAMOST spectra with low signal-to-noise ratios (SNR), which result in a sharp degradation on the accuracy of their estimations. Therefore, it is necessary to explore better estimation methods for low-SNR spectra. This paper proposed a neural network-based scheme to deliver atmospheric parameters, LASSO-MLPNet. Firstly, we adopt a polynomial fitting method to obtain pseudo-continuum and remove it. Then, some parameter-sensitive features in the existence of high noises were detected using Least Absolute Shrinkage and Selection Operator (LASSO). Finally, LASSO-MLPNet used a Multilayer Perceptron network (MLPNet) to estimate atmospheric parameters $T_{\mathrm{eff}}$, log $g$ and [Fe/H]. The effectiveness of the LASSO-MLPNet was evaluated on some LAMOST stellar spectra of the common star between APOGEE (The Apache Point Observatory Galactic Evolution Experiment) and LAMOST. it is shown that the estimation accuracy is significantly improved on the stellar spectra with $10<\mathrm{SNR}\leq80$. Especially, LASSO-MLPNet reduces the mean absolute error (MAE) of the estimation of $T_{\mathrm{eff}}$, log $g$ and [Fe/H] from (144.59 K, 0.236 dex, 0.108 dex) (LASP) to (90.29 K, 0.152 dex, 0.064 dex) (LASSO-MLPNet) on the stellar spectra with $10<\mathrm{SNR}\leq20$. To facilitate reference, we release the estimates of the LASSO-MLPNet from more than 4.82 million stellar spectra with $10<\mathrm{SNR}\leq80$ and 3500 < SNR$g$ $\leq$ 6500 as a value-added output.

preprint2022arXiv

Nonlinear Reduced DNN Models for State Estimation

We propose in this paper a data driven state estimation scheme for generating nonlinear reduced models for parametric families of PDEs, directly providing data-to-state maps, represented in terms of Deep Neural Networks. A major constituent is a sensor-induced decomposition of a model-compliant Hilbert space warranting approximation in problem relevant metrics. It plays a similar role as in a Parametric Background Data Weak framework for state estimators based on Reduced Basis concepts. Extensive numerical tests shed light on several optimization strategies that are to improve robustness and performance of such estimators.

preprint2022arXiv

Zero-Shot Multi-Modal Artist-Controlled Retrieval and Exploration of 3D Object Sets

When creating 3D content, highly specialized skills are generally needed to design and generate models of objects and other assets by hand. We address this problem through high-quality 3D asset retrieval from multi-modal inputs, including 2D sketches, images and text. We use CLIP as it provides a bridge to higher-level latent features. We use these features to perform a multi-modality fusion to address the lack of artistic control that affects common data-driven approaches. Our approach allows for multi-modal conditional feature-driven retrieval through a 3D asset database, by utilizing a combination of input latent embeddings. We explore the effects of different combinations of feature embeddings across different input types and weighting methods.

preprint2021arXiv

A hyper-reduced MAC scheme for the parametric Stokes and Navier-Stokes equations

The need for accelerating the repeated solving of certain parametrized systems motivates the development of more efficient reduced order methods. The classical reduced basis method is popular due to an offline-online decomposition and a mathematically rigorous {\em a posterior} error estimator which guides a greedy algorithm offline. For nonlinear and nonaffine problems, hyper reduction techniques have been introduced to make this decomposition efficient. However, they may be tricky to implement and often degrade the online computation efficiency. To avoid this degradation, reduced residual reduced over-collocation (R2-ROC) was invented integrating empirical interpolation techniques on the solution snapshots and well-chosen residuals, the collocation philosophy, and the simplicity of evaluating the hyper-reduced well-chosen residuals. In this paper, we introduce an adaptive enrichment strategy for R2-ROC rendering it capable of handling parametric fluid flow problems. Built on top of an underlying Marker and Cell (MAC) scheme, a novel hyper-reduced MAC scheme is therefore presented and tested on Stokes and Navier-Stokes equations demonstrating its high efficiency, stability and accuracy.

preprint2021arXiv

High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. Based on the framework of strong stability-preserving Runge-Kutta approach, we propose two high-order multirate explicit time-stepping schemes (SSPRK2-SE and SSPRK3-SE) for the resulting split system in this paper. The proposed schemes allow for a large time step to be used for the three-dimensional baroclinic (slow) mode and a small time step for the two-dimensional barotropic (fast) mode, in which each of the two mode solves just need to satisfy their respective CFL conditions for numerical stability. Specifically, at each time step, the baroclinic velocity is first computed by advancing the baroclinic mode and fluid thickness of the system with the large time-step \textcolor{black}{and the assistance of some intermediate approximations of the baroctropic mode obtained by substepping with the small-time step}; then the barotropic velocity is corrected by using the small time step to re-advance the barotropic mode under an improved barotropic forcing produced by interpolation of the forcing terms from the preceding baroclinic mode solves; lastly, the fluid thickness is updated by coupling the baroclinic and barotropic velocities. Additionally, numerical inconsistencies on the discretized sea surface height caused by the mode splitting are relieved via a reconciliation process with carefully calculated flux deficits. Two benchmark tests from the "MPAS-Ocean" platform are carried out to numerically demonstrate the performance and parallel scalability of the proposed SSPRK-SE schemes.

preprint2021arXiv

Structure-Preserving Galerkin POD-DEIM Reduced-Order Modeling of Hamiltonian Systems

A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but modifies the reduced order model so that the appropriate Hamiltonian structure is preserved. However, its computational complexity for online simulations is still high if the Hamiltonian involves non-polynomial nonlinearities. In this paper, we apply the discrete empirical interpolation method to improve the online efficiency of the structure-preserving reduced order simulations. Since the reduced basis truncation can degrade the Hamiltonian approximation, we propose to use the basis obtained from shifted snapshots. A nonlinear wave equation is used as a test bed and the numerical results illustrate the efficacy of the proposed method.

preprint2020arXiv

A Virtual Obstacle Course within Diverse Sensory Environments

We developed a novel assessment platform with untethered virtual reality, 3-dimensional sounds, and pressure sensing floor mat to help assess the walking balance and negotiation of obstacles given diverse sensory load and/or cognitive load. The platform provides an immersive 3D city-like scene with anticipated/unanticipated virtual obstacles. Participants negotiate the obstacles with perturbations of: auditory load by spatial audio, cognitive load by a memory task, and visual flow by generated by avatars movements at various amounts and speeds. A VR headset displays the scenes while providing real-time position and orientation of the participant's head. A pressure-sensing walkway senses foot pressure and visualizes it in a heatmap. The system helps to assess walking balance via pressure dynamics per foot, success rate of crossing obstacles, available response time as well as head kinematics in response to obstacles and multitasking. Based on the assessment, specific balance training and fall prevention program can be prescribed.

preprint2020arXiv

POD-(H)DG Method for Incompressible Flow Simulations

We present a reduced order method (ROM) based on proper orthogonal decomposition (POD) for the viscous Burgers' equation and the incompressible Navier-Stokes equations discretized using an implicit-explicit hybrid discontinuous Galerkin/discoutinuous Galerkin (IMEX HDG/DG) scheme. A novel closure model, which can be easily computed offline, is introduced. Numerical results are presented to test the proposed POD model and the closure model.

preprint2016arXiv

An Evolve-Then-Filter Regularized Reduced Order Model

In this paper, we propose a new evolve-then-filter reduced order model (EF-ROM). This is a regularized ROM (Reg-ROM), which aims at the numerical stabilization of proper orthogonal decomposition (POD) ROMs for convection-dominated flows. We also consider the Leray ROM (L-ROM). These two Reg-ROMs use explicit ROM spatial filtering to smooth (regularize) various terms in the ROMs. Two spatial filters are used: a POD projection onto a POD subspace (Proj) and a new POD differential filter (DF). The four Reg-ROM/filter combinations are tested in the numerical simulation of the three-dimensional flow past a circular cylinder at a Reynolds number $Re=1000$. Overall, the most accurate Reg-ROM/filter combination is EF-ROM-DF. Furthermore, the spatial filter has a higher impact on the Reg-ROM than the regularization used. Indeed, the DF generally yields better results than Proj for both the EF-ROM and L-ROM. Finally, the CPU times of the four Reg-ROM/filter combinations are orders of magnitude lower than the CPU time of the DNS.

preprint2016arXiv

FreeSense:Indoor Human Identification with WiFi Signals

Human identification plays an important role in human-computer interaction. There have been numerous methods proposed for human identification (e.g., face recognition, gait recognition, fingerprint identification, etc.). While these methods could be very useful under different conditions, they also suffer from certain shortcomings (e.g., user privacy, sensing coverage range). In this paper, we propose a novel approach for human identification, which leverages WIFI signals to enable non-intrusive human identification in domestic environments. It is based on the observation that each person has specific influence patterns to the surrounding WIFI signal while moving indoors, regarding their body shape characteristics and motion patterns. The influence can be captured by the Channel State Information (CSI) time series of WIFI. Specifically, a combination of Principal Component Analysis (PCA), Discrete Wavelet Transform (DWT) and Dynamic Time Warping (DTW) techniques is used for CSI waveform-based human identification. We implemented the system in a 6m*5m smart home environment and recruited 9 users for data collection and evaluation. Experimental results indicate that the identification accuracy is about 88.9% to 94.5% when the candidate user set changes from 6 to 2, showing that the proposed human identification method is effective in domestic environments.

preprint2015arXiv

Approximate Deconvolution Reduced Order Modeling

This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a POD differential filter is used to define the large ROM structures. An approximate deconvolution(AD) approach is used to solve the ROM closure problem and develop a new AD-ROM. This AD-ROM is tested in the numerical simulation of the one-dimensional Burgers equation with a small diffusion coefficient(10^{-3})

preprint2015arXiv

Influence of oxygen on thermal stability of nanocrystalline aluminum studied by positron annihilation spectroscopy

The thermal stability of nanocrystalline (nc) Al has been studied by means of positron lifetime spectroscopy and X-ray diffraction (XRD), prepared by compacting nanoparticles under high pressures. Those nanoparticles were produced by the flow-levitation (FL) method [1] and the arc-discharge (DC) method. Effect of oxide at nanoparticle surface on structure stability was investigated especially in this experiment. The positron lifetime results reveal that vacancy clusters in grain boundaries are dominant positron traps according to the high relative intensity of the positron lifetime τ2 in both samples. The mean grain size of the sample consisting of nanoparticles with partially oxidized surfaces is almost unchanged after aging at 150 for 84 h, with that of the sample consisting of pure nc Al increasing. The partially oxidized surfaces of nanoparticles hinder the growth of grain when aging at 150, vacancy clusters related to Al2O3 need longer aging time to decompose, which implies that the oxide stabilizes the microstructure of the nanomaterials. The effect is beneficial for nc materials to keep excellent properties.

preprint2015arXiv

Optical Tuning of Exciton and Trion Emissions in Monolayer Phosphorene

Monolayer phosphorene provides a unique two-dimensional (2D) platform to investigate the fundamental dynamics of excitons and trions (charged excitons) in reduced dimensions. However, owing to its high instability, unambiguous identification of monolayer phosphorene has been elusive. Consequently, many important fundamental properties, such as exciton dynamics, remain underexplored. We report a rapid, noninvasive, and highly accurate approach based on optical interferometry to determine the layer number of phosphorene, and confirm the results with reliable photoluminescence measurements. Furthermore, we successfully probed the dynamics of excitons and trions in monolayer phosphorene by controlling the photo-carrier injection in a relatively low excitation power range. Based on our measured optical gap and the previously measured electronic energy gap, we determined the exciton binding energy to be ~0.3 eV for the monolayer phosphorene on SiO2/Si substrate, which agrees well with theoretical predictions. A huge trion binding energy of ~100 meV was first observed in monolayer phosphorene, which is around five times higher than that in transition metal dichalcogenide (TMD) monolayer semiconductor, such as MoS2. The carrier lifetime of exciton emission in monolayer phosphorene was measured to be ~220 ps, which is comparable to those in other 2D TMD semiconductors. Our results open new avenues for exploring fundamental phenomena and novel optoelectronic applications using monolayer phosphorene.

preprint2014arXiv

A variational approach to the inverse photolithography problem

Photolithography is a process in the production of integrated circuits in which a mask is used to create an exposed pattern with a desired geometric shape. In the inverse problem of photolithography, a desired pattern is given and the mask that produces an exposed pattern which is close to the desired one is sought. We propose a variational approach formulation of this shape design problem and introduce a regularization strategy. The main novelty in this work is the regularization term that makes the thresholding operation involved in photolithography stable. The potential of the method is demonstrated in numerical experiments.

preprint2014arXiv

Atomically Thin Optical Lenses and Gratings

Two-dimensional (2D) materials have emerged as promising candidates for miniaturized optoelectronic devices, due to their strong inelastic interactions with light. On the other hand, a miniaturized optical system also requires strong elastic light-matter interactions to control the flow of light. Here, we report giant optical path length (OPL) from a single-layer molybdenum disulfide (MoS2), which is around one order of magnitude larger than that from a single-layer graphene. Using such giant OPL to engineer the phase front of optical beams, we demonstrated, to the best of our knowledge, the world's thinnest optical lens consisting of a few layers of MoS2 less than 6.3 nm thick. Moreover, we show that MoS2 has much better dielectric response than good conductor (like gold) and other dielectric materials (like Si, SiO2 or graphene). By taking advantage of the giant elastic scattering efficiency in ultra-thin high-index 2D materials, we demonstrated high-efficiency gratings based on a single- or few-layers of MoS2. The capability of manipulating the flow of light in 2D materials opens an exciting avenue towards unprecedented miniaturization of optical components and the integration of advanced optical functionalities.

preprint2014arXiv

Extraordinarily bound quasi-one-dimensional trions in two-dimensional phosphorene atomic semiconductors

The anisotropic nature of the new two-dimensional (2D) material phosphorene, in contrast to other 2D materials such as graphene and transition metal dichalcogenide (TMD) semiconductors, allows excitons to be confined in a quasi-one-dimensional (1D) space predicted in theory, leading to remarkable phenomena arising from the reduced dimensionality and screening. Here, we report a trion (charged exciton) binding energy of 190 meV in few-layer phosphorene at room temperature, which is nearly one to two orders of magnitude larger than those in 2D TMD semiconductors (20-30 meV) and quasi-2D quantum wells (1-5 meV). Such a large binding energy has only been observed in truly 1D materials such as carbon nanotubes, whose optoelectronic applications have been severely hurdled by their intrinsically small optical cross-sections. Phosphorene offers an elegant way to overcome this hurdle by enabling quasi-1D excitonic and trionic behaviors in a large 2D area, allowing optoelectronic integration. We experimentally validated the quasi-1D nature of excitonic and trionic dynamics in phospherene by demonstrating completely linearly polarized light emission from excitons and trions. The implications of the extraordinarily large trion binding energy in a higher-than-one-dimensional material are far-reaching. It provides a room-temperature 2D platform to observe the fundamental many-body interactions in the quasi-1D region. The strong photoluminescence emission in phosphorene has been electrically tuned over a large spectral range at room temperature, which opens a new route for tunable light sources.

preprint2014arXiv

Unambiguous identification of monolayer phosphorene by phase-shifting interferometry

Monolayer phosphorene provides a unique two-dimensional (2D) platform to investigate the fundamental many-body interactions. However, owing to its high instability, unambiguous identification of monolayer phosphorene has been elusive. Consequently, many important fundamental properties, such as exciton dynamics, remain underexplored. We report a rapid, noninvasive, and highly accurate approach based on optical interferometry to determine the layer number of phosphorene, and confirm the results with reliable photoluminescence measurements. Based on the measured optical gap and the calculated electronic energy gap, we determined the exciton binding energy to be ~0.4 eV for the monolayer phosphorene on SiO2/Si substrate, which agrees well with theoretical predictions. Our results open new avenues for exploring fundamental phenomena and novel optoelectronic applications using monolayer phosphorene.

preprint2013arXiv

Are the Snapshot Difference Quotients Needed in the Proper Orthogonal Decomposition?

This paper presents a theoretical and numerical investigation of the following practical question: Should the time difference quotients of the snapshots be used to generate the proper orthogonal decomposition basis functions? The answer to this question is important, since some published numerical studies use the time difference quotients, whereas other numerical studies do not. The criterion used in this paper to answer this question is the rate of convergence of the error of the reduced order model with respect to the number of proper orthogonal decomposition basis functions. Two cases are considered: the no_DQ case, in which the snapshot difference quotients are not used, and the DQ case, in which the snapshot difference quotients are used. The error estimates suggest that the convergence rates in the $C^0(L^2)$-norm and in the $C^0(H^1)$-norm are optimal for the DQ case, but suboptimal for the no_DQ case. The convergence rates in the $L^2(H^1)$-norm are optimal for both the DQ case and the no_DQ case. Numerical tests are conducted on the heat equation and on the Burgers equation. The numerical results support the conclusions drawn from the theoretical error estimates. Overall, the theoretical and numerical results strongly suggest that, in order to achieve optimal pointwise in time rates of convergence with respect to the number of proper orthogonal decomposition basis functions, one should use the snapshot difference quotients.

preprint2013arXiv

Nonlinear Model Reduction Based On The Finite Element Method With Interpolated Coefficients: Semilinear Parabolic Equations

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its computational efficiency, which, however, is its the most significant advantage. Nonlinear dimensional reduction methods, such as the discrete empirical interpolation method, have been widely used to evaluate the nonlinear terms at a low cost. But when the finite element method is utilized for the spatial discretization, nonlinear snapshot generation requires inner products to be fulfilled, which costs lots of off-line time. Numerical integrations are also needed over elements sharing the selected interpolation points during the simulation, which keeps on-line time high. In this paper, we extend the finite element method with interpolated coefficients to nonlinear reduced-order models. It approximates the nonlinear function in the reduced-order model by its finite element interpolation, which makes coefficient matrices of the nonlinear terms pre-computable and, thus, leads to great savings in the computational efforts. Due to the separation of spatial and temporal variables in the finite element interpolation, the discrete empirical interpolation method can be directly applied on the nonlinear functions. Therefore, the main computational hurdles when applying the discrete empirical interpolation method in the finite element context are conquered. We also establish a rigorous asymptotic error estimation, which shows that the proposed approach achieves the same accuracy as that of the standard finite element method under certain smoothness assumptions of the nonlinear functions. Several numerical tests are presented to validate the proposed method and verify the theoretical results.

preprint2013arXiv

Variational Multiscale Proper Orthogonal Decomposition: Navier-Stokes Equations

We develop a variational multiscale proper orthogonal decomposition reduced-order model for turbulent incompressible Navier-Stokes equations. The error analysis of the full discretization of the model is presented. All error contributions are considered: the spatial discretization error (due to the finite element discretization), the temporal discretization error (due to the backward Euler method), and the proper orthogonal decomposition truncation error. Numerical tests for a three-dimensional turbulent flow past a cylinder at Reynolds number Re=1000 show the improved physical accuracy of the new model over the standard Galerkin and mixing-length proper orthogonal decomposition reduced-order models. The high computational efficiency of the new model is also showcased. Finally, the theoretical error estimates are confirmed by numerical simulations of a two-dimensional Navier-Stokes problem.

preprint2012arXiv

A Finite Element Discretization of the Streamfunction Formulation of the Stationary Quasi-Geostrophic Equations of the Ocean

This paper presents a conforming finite element discretization of the streamfunction formulation of the one-layer stationary quasi-geostrophic equations, which are a commonly used model for the large scale wind- driven ocean circulation. Optimal error estimates for this finite element discretization with the Argyris element are derived. Numerical tests for the finite element discretization of the quasi-geostrophic equations and two of its standard simplifications (the linear Stommel model and the linear Stommel-Munk model) are carried out. By benchmarking the numerical results against those in the published literature, we conclude that our finite element discretization is accurate. Furthermore, the numerical results have the same convergence rates as those predicted by the theoretical error estimates.

preprint2011arXiv

Approximate deconvolution large eddy simulation of a barotropic ocean circulation model

This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does not employ additional phenomenological arguments to the model. The new approximate deconvolution model is tested in the numerical simulation of the wind-driven circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics. The model employs the barotropic vorticity equation driven by a symmetric double-gyre wind forcing, which yields a four-gyre circulation in the time mean. The approximate deconvolution model yields the correct four-gyre circulation structure predicted by a direct numerical simulation, on a coarser mesh but at a fraction of the computational cost. This first step in the numerical assessment of the new model shows that approximate deconvolution could represent a viable tool for under-resolved computations in the large eddy simulation of more realistic turbulent geophysical flows.

preprint2011arXiv

Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison

This paper puts forth two new closure models for the proper orthogonal decomposition reduced-order modeling of structurally dominated turbulent flows: the dynamic subgrid-scale model and the variational multiscale model. These models, which are considered state-of-the-art in large eddy simulation, together with the mixing length and the Smagorinsky closure models, are tested in the numerical simulation of a 3D turbulent flow around a circular cylinder at Re = 1,000. Two criteria are used in judging the performance of the proper orthogonal decomposition reduced-order models: the kinetic energy spectrum and the time evolution of the POD coefficients. All the numerical results are benchmarked against a direct numerical simulation. Based on these numerical results, we conclude that the dynamic subgrid-scale and the variational multiscale models perform best.

preprint2011arXiv

Variational Multiscale Proper Orthogonal Decomposition: Convection-Dominated Convection-Diffusion Equations

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested for convection-dominated convection-diffusion equations. The numerical analysis of the finite element discretization of the model is presented. Numerical tests show the increased numerical accuracy over the standard reduced-order model and illustrate the theoretical convergence rates.